求导：f(x)=(e^x+1)/e^x

题目

求导：f(x)=(e^x+1)/e^x

答案

f(x)=(e^x+1)/e^x = 1 + 1/e^x = 1 + e^(-x)
f '(x) = [1 + e^(-x)] '
= [e^(-x)] '
=[e^(-x)]*(-x)'
=[e^(-x)]*(-1)
= -e^(-x)
= -1/e^x,即f '(x) = -1/e^x